Sub-Nyquist Modulo Sampling Of Fri Signals

In this demo, we present a hardware prototype for sub-Nyquist sampling and reconstruction for FRI signals under modulo constraint. In the conventional analog to digital conversion (ADC) systems, the sampling rate is twice the bandwidth of the signal to be sampled. Further, it is assumed that the signal’s dynamic range is within the dynamic range of the ADC. However, in many applications, such as radar and ultrasound imaging, the bandwidth of the received signals could be very high and their dynamic range could be beyond that of the ADC. In this demo, we address the issues of high-sampling rates and the dynamic range by exploring the structure in the received signal. In particular, the received signal has a finite rate of innovation and can be sampled at a sub-Nyquist rate [1]. Further, to avoid clipping, a modulo operation is performed on the received signal before sampling [2]. By combining these methods, we devise a sampling and reconstruction strategy that leads to a perfect reconstruction while operating at a sub-Nyquist rate. We demonstrate the above-mentioned sampling framework through a hardware prototype. Our system consists of the following components: (1) a vector signal generator for the FRI signals, (2) a modulo operator that is built by using a set of comparators, (3) a sub-Nyquist sampler. Once the samples are acquired, the FRI signal parameters are estimated by applying the reconstruction algorithm. The prototype will be presented along with a dedicated GUI depicting the computed performance measures and allowing comparison to sub-Nyquist with and without modulo operation. References: [1] R. Tur, Y. C. Eldar, and Z. Friedman, "Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging," IEEE Trans. Signal Process., 2011. [2] A. Bhandari, F. Krahmer and R. Raskar, "Unlimited Sampling of Sparse Signals," ICASSP 2018.